Sensitivity analysis of microseismic positioning accuracy based on distribution models of influencing factors

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1 46 9 ( ) Vol.46 No Joural of Cetral South Uiversity (Sciece ad Techology) Sep. 15 DOI: /j.iss ( 183) V e T e D e 3 TU46 A (15) Sesitivity aalysis of microseismic positioig accuracy based o distributio models of ifluecig factors GAO Yogtao, WU Qigliag, WU Shuchua, YANG Kai, DOU Lipig, YAO Pegfei (Key Laboratory of the Miistry of Educatio of Chia for High-Efficiet Miig ad Safety of Metal Mies, School of Civil & Eviromet Egieerig, Uiversity of Sciece ad Techology Beijig, Beijig 183, Chia) Abstract: Based o microseismic positioig equatio ad miimum error priciple, a iput ad output mathematical model for evaluatig sesitivity of microseismic positioig accuracy was costructed. Distace error betwee microseismic sources ad sesors, seismic wave velocity error ad trigger times error were selected as aalysis factors. Factor distributio factio was discussed by usig iformatio etropy, ad the correspodig expressio was obtaied by fuctioal variatio. Scheme of 16 groups was desiged by usig orthogoal method. Level value of each factor was give accordig to the factor distributio fuctio. Ad the global sesitivity aalysis was performed. The results show that three factors accord with uiform distributio i a give iterval; for both the iteral ad exteral field sources, seismic wave velocity error is the most ifluetial factor that affects the positioig results, ad the sigificat order from big to small of ifluece o positioig accuracy is V e T e ad D e. For iteral field source, all three factors have some sigificat ifluece o positioig accuracy; while for the exteral field source, oly the seismic wave velocity error has some sigificat ifluece o positioig accuracy, which may probably be affected by the iteractio betwee the factors or experimetal errors. The research coclusios may offer specific guidace for the accurate locatio aalysis of microseismic moitorig i the similar projects. Key words: microseismic; positioig accuracy; sesitivity; distributio model; errors (Foudatio item)(irt95)(frf-sd-1-a) (Project(IRT95) supported by the Program for Chagjiag Scholars ad Iovative Research Team i Uiversity; Project(FRF-SD-1-A) supported by the Fudametal Research Fuds for the Cetral Uiversities) wuqigliagmy@163.com

2 343 ( ) 46 [1 3] ( ) ( ) Garso [4] [5] [6 1] [1] (PaD) [11] (LH-OAT) [1] 1 ( x, y, z ) ii ( = 1,, ) ( xi, yi, zi ) d i i i i i d = ( x x ) + ( y y ) + ( z z ), ( i = 1,,, ) (1) t t i ( ) v d v i + t = ti,( i = 1,,, ) () () 3 () ( di, v, ti) ( di, v, t i ) ξ ij (i=1,,, ; j=1,, 3) d + v t i = di ξi1 = v + ξi i = ti + ξi3 (3) i i i ) i1 ( x x ) + ( y y ) + ( z z ξ i i i3 (3) ( v ξ ) ( t t ξ ) =, ( i = 1,, ) (4) ξ ij ( i = 1,, ; j = 1,,3) ξ ij ( i = 1,,, ; j = 1,,3) ξ = (4) ( x, y, z, t ) ij 1 mi ϕ( x, y, z, t) = ξij (5) i= 1 ξij τij ( x, y, z, v, t, xi, yi, zi ) = (i=1,,, ; j=1,, 3) ϑ( X ) (5) 1 T 1 Ψ ( X) = ϑ( X) ϑ ( X) = τij ( x, y, z, t) (6) i= 1 Ψ ( X ) X (5) 1 T Ψ ( X ) = mi Ψ ( X) = mi ϑ( X) ϑ( X ) X R X R X = [ x y z t ] T D e V e T e 3 α 1, α,, α

3 P1, P,, P H = P P P P P l P (7) 1l 1 l = H = P( α)l P( α ) = = 1 P( α ) P( α ) l α Δ Δ α = P( α) P( α) l P( α )l Δ α = = lim H = p ( α )l p ( α )d α lim l (9) p( ) lim P( α α = ) (8) (9) H + l H = p( α)l p( α)dα (1) [a, b] b p ( α )d α = 1 a δ H = J = p( α)l p( α) + λp( α) (11) ( ) [a, b] p( α) m m 1 α ( k = 1,, m) k αk k 1 p( α)d α= (14) a m L16(4 5 ) 1 1 Table 1 Desig scheme based o orthogoal desig 1 D e1 V e1 T e1 9 D e3 V e1 T e3 D e1 V e T e 1 D e3 V e T e4 3 D e1 V e3 T e3 11 D e3 V e3 T e1 4 D e1 V e4 T e4 1 D e3 V e4 T e 5 D e V e1 T e 13 D e4 V e1 T e4 6 D e V e T e1 14 D e4 V e T e3 7 D e V e3 T e4 15 D e4 V e3 T e 8 D e V e4 T e3 16 D e4 V e4 T e1 4 J d ( J p ) = (1) p dα p = p( α) 1, a α b p( α) = b a (13), α < a α > b (13) 3 O 6 6 ( m) A( 5 5) B(5 5) C(1 5 5) D(5 1 5) E(5 5 1 ) F(5 5 ) H( ) I( ) v=5. m/ms 1::: 1 1 (BMS) 1 a [13] D e (m) V e (m/ms) T e (ms) 3

4 343 ( ) 46 1 Fig. 1 Distributio of sesors ad microseismic sources [, 6] [, 6% ] [, 3] 3 4 ( 16 ) 3 v m /m( r ) 5.1 () K jk j k K jk K jk R j j j R j 4 5 R j 1 R j V e T e D e V e T e D e ( 1 3 )( 4 ) () () 3 4 Table Value of three factors ad four levels of iteral ad exteral field sources usig orthogoal desig 3 H I 4 4 (1) () (3) (4) (1) () (3) (4) A B C D E F A B C D E F

5 Table 3 Positioig results of iteral ad exteral field sources m H I x =3. y =64. z =746. x =673. y =7. z =1. 1 D e1 V e1 T e D e1 V e T e D e1 V e3 T e D e1 V e4 T e D e V e1 T e D e V e T e D e V e3 T e D e V e4 T e D e3 V e1 T e D e3 V e T e D e3 V e3 T e D e3 V e4 T e D e4 V e1 T e D e4 V e T e D e4 V e3 T e D e4 V e4 T e Table 4 Rage aalysis of test results for iteral field source D e V e T e

6 3434 ( ) 46 4 K j K j K j K j K j K j { 1 L L } { K j1 L K jk L K jm} R = max K, K, K j j jk jm mi,, K j K j R j Table 5 Rage aalysis of test results for exteral field source D e V e T e K j K j K j K j K j K j K j K j { 1 L L } { K j1 L K jk L K jm} R = max K, K, K j j jk jm mi,, R j

7 m 1 i i= 1 r k= 1 5. ( ) Se = x K jk (19) 1 f j f e j 6 7 F 6 F D e = (3,3) ST = Sj+ Se (15) F 55 V e = F.1 (3,3) F T = e (3,3) M j Sj / f j F = = ~ F (, ) α f j fe (16) Me Se / fe 6 S T V e T e D e 7 1 ST = ( xi x) = xi ( x i ) (17) i= 1 i= 1 i= 1 S j j V e T e D e F m m 1 1 F D e = (3,3) 5.39 F V e = j ( K jk ) jk ( i ) k 1 r K x (18) = k= 1 i= 1 F.1(3,3) = F T e = 4.94 F. 1 (3,3) = 5.39 S e ( ) 6 Table 6 Variace aalysis of test results for iteral field source ( ) F F α F.1 (3,3)=9.457 ** F.5 (3,3)=9.8 ** F.1 (3,3)=5.39 ** e Table 7 Variace aalysis of test results for exteral field source ( ) F F α F.1 (3,3)= F.5 (3,3)=9.8 ** F.1 (3,3)=5.39 e

8 3436 ( ) ) D e V e T e 3 ) 16 V e T e D e 3) 3 V e T e D e [1],,,. TBM [J]., 11, 3(): CHEN Bigrui, FENG Xiatig, ZENG Xioghui, et al. Real-time microseismic moitorig ad its characteristic aalysis durig TBM tuelig i deep-buried tuel[j]. Chiese Joural of Rock Mechaics ad Egieerig, 11, 3(): [],,,. [J]., 1, 31(5): ZHANG Bohu, DENG Jiahui, GAO Migzhog, et al. Safety evaluatio research based o microseismic moitorig i udergroud powerhouse of hydropower statio[j]. Chiese Joural of Rock Mechaics ad Egieerig, 1, 31(5): [3],,,. [J]., 1, 41(1): 5. DOU Limig, HE Jiag, GONG Siyua, et al. A case study of micro-seismic moitorig: goaf water-irush dyamic hazards[j]. Joural of Chia Uiversity of Miig & Techology, 1, 41(1): 5. [4] Garso G D. Iterpretig eural-etwork coectio weights[j]. Artificial Itelligece Expert, 1991, 6(4): [5] Olde J D, Jackso D A. Illumiatig the black box : A radomizatio approach for uderstadig variable cotributios i artificial eural etworks[j]. Ecological Modellig,, 154(1): [6] Borgoovo E, Peccati L. Ucertaity ad global sesitivity aalysis i the evaluatio of ivestmet projects[j]. Iteratioal Joural of Productio Ecoomics, 6, 14(1): [7],,,. EasyDHM( ): [J]., 1, 41(8): LEI Xiaohui, JIANG Yuzhog, WANG Hao, et al. Distributed hydrological model EasyDHM. Applicatio[J]. Joural of Hydraulic Egieerig, 1, 41(8): [8],,,. [J]., 1, 3(5): SONG Xiaomeg, KONG Fazhe, ZHAN Chesheg, et al. Sesitivity aalysis of hydrological model parameters usig a statistical theory approach[j]. Advaces i Water Sciece, 1, 3(5): [9],,. (FAST) [J]., 1, 43(): JIN Xiaofei, FAN Feg, SHEN Shizhao, et al. Parameter sesitivity aalysis of the cable-et structure supportig the reflector of a large radio telescope-fast[j]. Chia Civil Egieerig Joural, 1, 43(): [1] Sobol I M. Sesitivity estimates for oliear mathematical models[j]. Math Modelig & Computatioal Experimet, 1993(1): [11] Gevrey M, Dimopoulos I, Lek S. Two-way iteractio of iput variables i the sesitivity aalysis of eural etwork models[j]. Ecological Modellig, 6, 195(1): [1] va Griesve A, Meixer T, Gruwald S, et al. A global sesitivity aalysis tool for the parameters of multi-variable catchmet models[j]. Joural of Hydrology, 6, 34(1): 1 3. [13],,,. D [J]., 13, 35(1): GAO Yogtao, WU Qigliag, WU Shuchua, et al. Optimizatio of microseismic moitorig etwork based o the theory of D-optimal desig[j]. Joural of Uiversity of Sciece ad Techology Beijig, 13, 35(1): ( )

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